Permutations (1 Viewer)

[Deliriously]

Find the number of ways in which the word EPSILON can be arranged in a row so that three vowels are all next to each other. I got a different answer. Is there some trap to this question?

 

[Deliriously]

ah I had 3! x 5!
the answers says (4 x 3!) x 4!

 

[lolcakes52]

Part 1:
So consider the three vowels as a unit, because they have to be next to each other. They can be arranged in 3! ways.

Part 2:
Now there are seven letters in total, but when we consider the vowels as a single unit we could say that there are 5 units, the three vowels and each of the four individual consonants. These units can be arranged in 5! ways.

Part 3 :
3!*5! = anwser

 

[Deliriously]

Part 1:
So consider the three vowels as a unit, because they have to be next to each other. They can be arranged in 3! ways.

Part 2:
Now there are seven letters in total, but when we consider the vowels as a single unit we could say that there are 5 units, the three vowels and each of the four individual consonants. These units can be arranged in 5! ways.

Part 3 :
3!*5! = anwser

Yup, that's how I interpreted the question.